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of 168
pro vyhledávání: '"Walk, Harro"'
In this paper we revisit the classical method of partitioning classification and study its convergence rate under relaxed conditions, both for observable (non-privatised) and for privatised data. Let the feature vector $X$ take values in $\mathbb{R}^
Externí odkaz:
http://arxiv.org/abs/2312.14889
We study the problem of lossless feature selection for a $d$-dimensional feature vector $X=(X^{(1)},\dots ,X^{(d)})$ and label $Y$ for binary classification as well as nonparametric regression. For an index set $S\subset \{1,\dots ,d\}$, consider the
Externí odkaz:
http://arxiv.org/abs/2311.05033
We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss in estimating a random variable from an observed feature vector and the minimum expected loss in estimating the same random variabl
Externí odkaz:
http://arxiv.org/abs/2307.16735
We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size $n$ and re
Externí odkaz:
http://arxiv.org/abs/2307.09896
In this paper we analyze the $L_2$ error of neural network regression estimates with one hidden layer. Under the assumption that the Fourier transform of the regression function decays suitably fast, we show that an estimate, where all initial weight
Externí odkaz:
http://arxiv.org/abs/2107.09550
In this paper we revisit the classical problem of nonparametric regression, but impose local differential privacy constraints. Under such constraints, the raw data $(X_1,Y_1),\ldots,(X_n,Y_n)$, taking values in $\mathbb{R}^d \times \mathbb{R}$, canno
Externí odkaz:
http://arxiv.org/abs/2011.00216
Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient descent proc
Externí odkaz:
http://arxiv.org/abs/1912.03921
Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large probability neares
Externí odkaz:
http://arxiv.org/abs/1811.07133
$n$ independent random points drawn from a density $f$ in $R^d$ define a random Voronoi partition. We study the measure of a typical cell of the partition. We prove that the asymptotic distribution of the probability measure of the cell centered at a
Externí odkaz:
http://arxiv.org/abs/1512.04267
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